public TriangleData(Vector3 p1, Vector3 p2, Vector3 p3, Rigidbody boatRB, float timeSinceStart)
{
this.p1 = p1;
this.p2 = p2;
this.p3 = p3;
//Center of the triangle
this.center = (p1 + p2 + p3) / 3f;
//Distance to the surface from the center of the triangle
this.distanceToSurface = Mathf.Abs(WaterController.current.DistanceToWater(this.center, timeSinceStart));
//Normal to the triangle
this.normal = Vector3.Cross(p2 - p1, p3 - p1).normalized;
//Area of the triangle
this.area = BoatPhysicsMath.GetTriangleArea(p1, p2, p3);
//Velocity vector of the triangle at the center
this.velocity = BoatPhysicsMath.GetTriangleVelocity(boatRB, this.center);
//Velocity direction
this.velocityDir = this.velocity.normalized;
//Angle between the normal and the velocity
//Negative if pointing in the opposite direction
//Positive if pointing in the same direction
this.cosTheta = Vector3.Dot(this.velocityDir, this.normal);
}
//Calculate the area of each triangle in the boat mesh and store them in an array
private void CalculateOriginalTrianglesArea()
{
//Loop through all the triangles (3 vertices at a time = 1 triangle)
int i = 0;
int triangleCounter = 0;
while (i < boatTriangles.Length)
{
Vector3 p1 = boatVertices[boatTriangles[i]];
i++;
Vector3 p2 = boatVertices[boatTriangles[i]];
i++;
Vector3 p3 = boatVertices[boatTriangles[i]];
i++;
//Calculate the area of the triangle
float triangleArea = BoatPhysicsMath.GetTriangleArea(p1, p2, p3);
//Store the area in a list
slammingForceData[triangleCounter].originalArea = triangleArea;
//The total area
boatArea += triangleArea;
triangleCounter += 1;
}
}
//Calculate the current velocity at the center of each triangle of the original boat mesh
private void CalculateSlammingVelocities(List <SlammingForceData> slammingForceData)
{
for (int i = 0; i < slammingForceData.Count; i++)
{
//Set the new velocity to the old velocity
slammingForceData[i].previousVelocity = slammingForceData[i].velocity;
//Center of the triangle in world space
Vector3 center = transform.TransformPoint(slammingForceData[i].triangleCenter);
//Get the current velocity at the center of the triangle
slammingForceData[i].velocity = BoatPhysicsMath.GetTriangleVelocity(boatRB, center);
}
}
//Add all forces that act on the squares above the water
void AddAboveWaterForces()
{
//Get all triangles
List <TriangleData> aboveWaterTriangleData = modifyBoatMesh.aboveWaterTriangleData;
//Loop through all triangles
for (int i = 0; i < aboveWaterTriangleData.Count; i++)
{
TriangleData triangleData = aboveWaterTriangleData[i];
//Calculate the forces
Vector3 forceToAdd = Vector3.zero;
//Force 1 - Air resistance
//Replace VisbyData.C_r with your boat's drag coefficient
forceToAdd += BoatPhysicsMath.AirResistanceForce(rhoAir, triangleData, 1f);
//Add the forces to the boat
boatRB.AddForceAtPosition(forceToAdd, triangleData.center);
//Debug
//The normal
//Debug.DrawRay(triangleCenter, triangleNormal * 3f, Color.white);
//The velocity
//Debug.DrawRay(triangleCenter, triangleVelocityDir * 3f, Color.black);
if (triangleData.cosTheta > 0f)
{
//Debug.DrawRay(triangleCenter, triangleVelocityDir * 3f, Color.black);
}
//Air resistance
//-3 to show it in the opposite direction to see what's going on
//Debug.DrawRay(triangleCenter, airResistanceForce.normalized * -3f, Color.blue);
}
}
//Build the new triangles where two of the old vertices are above the water
private void AddTrianglesTwoAboveWater(List <VertexData> vertexData, int triangleCounter)
{
//H and M are above the water
//H is after the vertice that's below water, which is L
//So we know which one is L because it is last in the sorted list
Vector3 L = vertexData[2].globalVertexPos;
//Find the index of H
int H_index = vertexData[2].index + 1;
if (H_index > 2)
{
H_index = 0;
}
//We also need the heights to water
float h_L = vertexData[2].distance;
float h_H = 0f;
float h_M = 0f;
Vector3 H = Vector3.zero;
Vector3 M = Vector3.zero;
//This means that H is at position 1 in the list
if (vertexData[1].index == H_index)
{
H = vertexData[1].globalVertexPos;
M = vertexData[0].globalVertexPos;
h_H = vertexData[1].distance;
h_M = vertexData[0].distance;
}
else
{
H = vertexData[0].globalVertexPos;
M = vertexData[1].globalVertexPos;
h_H = vertexData[0].distance;
h_M = vertexData[1].distance;
}
//Now we can find where to cut the triangle
//Point J_M
Vector3 LM = M - L;
float t_M = -h_L / (h_M - h_L);
Vector3 LJ_M = t_M * LM;
Vector3 J_M = LJ_M + L;
//Point J_H
Vector3 LH = H - L;
float t_H = -h_L / (h_H - h_L);
Vector3 LJ_H = t_H * LH;
Vector3 J_H = LJ_H + L;
//Save the data, such as normal, area, etc
//1 triangle above the water
underWaterTriangleData.Add(new TriangleData(L, J_H, J_M, boatRB, timeSinceStart));
//2 triangles below the water
aboveWaterTriangleData.Add(new TriangleData(J_H, H, J_M, boatRB, timeSinceStart));
aboveWaterTriangleData.Add(new TriangleData(J_M, H, M, boatRB, timeSinceStart));
//Calculate the submerged area
slammingForceData[triangleCounter].submergedArea = BoatPhysicsMath.GetTriangleArea(L, J_H, J_M);
indexOfOriginalTriangle.Add(triangleCounter);
}
//Build the new triangles where one of the old vertices is above the water
private void AddTrianglesOneAboveWater(List <VertexData> vertexData, int triangleCounter)
{
//H is always at position 0
Vector3 H = vertexData[0].globalVertexPos;
//Left of H is M
//Right of H is L
//Find the index of M
int M_index = vertexData[0].index - 1;
if (M_index < 0)
{
M_index = 2;
}
//We also need the heights to water
float h_H = vertexData[0].distance;
float h_M = 0f;
float h_L = 0f;
Vector3 M = Vector3.zero;
Vector3 L = Vector3.zero;
//This means M is at position 1 in the List
if (vertexData[1].index == M_index)
{
M = vertexData[1].globalVertexPos;
L = vertexData[2].globalVertexPos;
h_M = vertexData[1].distance;
h_L = vertexData[2].distance;
}
else
{
M = vertexData[2].globalVertexPos;
L = vertexData[1].globalVertexPos;
h_M = vertexData[2].distance;
h_L = vertexData[1].distance;
}
//Now we can calculate where we should cut the triangle to form 2 new triangles
//because the resulting area will always form a square
//Point I_M
Vector3 MH = H - M;
float t_M = -h_M / (h_H - h_M);
Vector3 MI_M = t_M * MH;
Vector3 I_M = MI_M + M;
//Point I_L
Vector3 LH = H - L;
float t_L = -h_L / (h_H - h_L);
Vector3 LI_L = t_L * LH;
Vector3 I_L = LI_L + L;
//Save the data, such as normal, area, etc
//2 triangles below the water
underWaterTriangleData.Add(new TriangleData(M, I_M, I_L, boatRB, timeSinceStart));
underWaterTriangleData.Add(new TriangleData(M, I_L, L, boatRB, timeSinceStart));
//1 triangle above the water
aboveWaterTriangleData.Add(new TriangleData(I_M, H, I_L, boatRB, timeSinceStart));
//Calculate the total submerged area
float totalArea = BoatPhysicsMath.GetTriangleArea(M, I_M, I_L) + BoatPhysicsMath.GetTriangleArea(M, I_L, L);
slammingForceData[triangleCounter].submergedArea = totalArea;
indexOfOriginalTriangle.Add(triangleCounter);
//Add 2 times because 2 submerged triangles need to connect to the same original triangle
indexOfOriginalTriangle.Add(triangleCounter);
}
//Add all forces that act on the squares below the water
void AddUnderWaterForces()
{
//The resistance coefficient - same for all triangles
float Cf = BoatPhysicsMath.ResistanceCoefficient(
rhoWater,
boatRB.velocity.magnitude,
modifyBoatMesh.CalculateUnderWaterLength());
//To calculate the slamming force we need the velocity at each of the original triangles
List <SlammingForceData> slammingForceData = modifyBoatMesh.slammingForceData;
CalculateSlammingVelocities(slammingForceData);
//Need this data for slamming forces
float boatArea = modifyBoatMesh.boatArea;
float boatMass = 1f; //Replace this line with your boat's total mass
//To connect the submerged triangles with the original triangles
List <int> indexOfOriginalTriangle = modifyBoatMesh.indexOfOriginalTriangle;
//Get all triangles
List <TriangleData> underWaterTriangleData = modifyBoatMesh.underWaterTriangleData;
for (int i = 0; i < underWaterTriangleData.Count; i++)
{
TriangleData triangleData = underWaterTriangleData[i];
//Calculate the forces
Vector3 forceToAdd = Vector3.zero;
//Force 1 - The hydrostatic force (buoyancy)
forceToAdd += BoatPhysicsMath.BuoyancyForce(rhoWater, triangleData);
//Force 2 - Viscous Water Resistance
forceToAdd += BoatPhysicsMath.ViscousWaterResistanceForce(rhoWater, triangleData, Cf);
//Force 3 - Pressure drag
forceToAdd += BoatPhysicsMath.PressureDragForce(triangleData);
//Force 4 - Slamming force
//Which of the original triangles is this triangle a part of
int originalTriangleIndex = indexOfOriginalTriangle[i];
SlammingForceData slammingData = slammingForceData[originalTriangleIndex];
forceToAdd += BoatPhysicsMath.SlammingForce(slammingData, triangleData, boatArea, boatMass);
//Add the forces to the boat
boatRB.AddForceAtPosition(forceToAdd, triangleData.center);
//Debug
//Normal
//Debug.DrawRay(triangleData.center, triangleData.normal * 3f, Color.white);
//Buoyancy
//Debug.DrawRay(triangleData.center, BoatPhysicsMath.BuoyancyForce(rhoWater, triangleData).normalized * -3f, Color.blue);
//Velocity
//Debug.DrawRay(triangleCenter, triangleVelocityDir * 3f, Color.black);
//Viscous Water Resistance
//Debug.DrawRay(triangleCenter, viscousWaterResistanceForce.normalized * 3f, Color.black);
}
}